{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7NFUPEXHDE4WQC25OOV7SLNGC7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5cb475411e625e75e50ac3013ac96c8047c188ef419549ef7647553f132f8c51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-09-28T11:24:32Z","title_canon_sha256":"def20bff91779e77bef57904fb20f0b4f8b96d127d824d02df6c641eeddd9f53"},"schema_version":"1.0","source":{"id":"1009.5534","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5534","created_at":"2026-05-18T03:55:21Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5534v2","created_at":"2026-05-18T03:55:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5534","created_at":"2026-05-18T03:55:21Z"},{"alias_kind":"pith_short_12","alias_value":"7NFUPEXHDE4W","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"7NFUPEXHDE4WQC25","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"7NFUPEXH","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:cd7066cd097e95e6617efeafdb55f34b1db861f55c730a0385cb976933636744","target":"graph","created_at":"2026-05-18T03:55:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"A completely new approach to the problem of energy distribution in statistical mechanics is developed that results in a general, combinatorial formula for the density of states. Relying on the approach the energy equipartition principle is reexamined and a new perspective on the theory of phase transitions (as resulting from nontrivial patterns of energy distribution characterized by the well-defined classes of forbidden microstates) is given.","authors_text":"Agata Fronczak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-09-28T11:24:32Z","title":"General, combinatorial formula for the density of states: insights into the energy equipartition principle and the theory of phase transitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5534","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:206ea5bde6ea8bb3cb865f4fd621499bcc016d25447d31633835ef0cf19c3b83","target":"record","created_at":"2026-05-18T03:55:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5cb475411e625e75e50ac3013ac96c8047c188ef419549ef7647553f132f8c51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-09-28T11:24:32Z","title_canon_sha256":"def20bff91779e77bef57904fb20f0b4f8b96d127d824d02df6c641eeddd9f53"},"schema_version":"1.0","source":{"id":"1009.5534","kind":"arxiv","version":2}},"canonical_sha256":"fb4b4792e71939680b5d73abf92da617f477e403e7fd7022b7ac043deaf33dcc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb4b4792e71939680b5d73abf92da617f477e403e7fd7022b7ac043deaf33dcc","first_computed_at":"2026-05-18T03:55:21.952251Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:21.952251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aKFNXat2/oTb3BxOOzu+dsit0K8RXEkQWHAaXC2uWrPPE3f8k5algJ0vawQqgsevDL8j/pQ1fNsg10B7/+D7CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:21.952923Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.5534","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:206ea5bde6ea8bb3cb865f4fd621499bcc016d25447d31633835ef0cf19c3b83","sha256:cd7066cd097e95e6617efeafdb55f34b1db861f55c730a0385cb976933636744"],"state_sha256":"82309dcfc1ad2858d006f736baa6ed4319fb36a70b094ad8921857ff3353a5aa"}